The name of City Councilor John R. Connolly dominates many political discussions these days in Bellevue Hill, a West Roxbury enclave of colonial homes and moss-covered stone walls where more people have voted in the last three mayoral elections than anywhere else in Boston.

A few neighborhoods over, in Dorchester, the fire-engine red yard signs of state Representative Martin J. Walsh flourish along Gallivan Boulevard like mayoral flags proudly planted by a local militia.

But the color of yard signs changes dramatically to a “reflex blue” along Cummins Highway and into Hyde Park, marking the home territory of another mayoral candidate, City Councilor Rob Consalvo. It was this high-voting, historically Italian neighborhood of tidy houses and petite lawns that helped keep Mayor Thomas M. Menino in office for two decades.

“Your neighborhood is going to go for your local guy,” said Frank Garibaldi, a 59-year-old Consalvo supporter who lives on Menino’s street in the Readville section of Hyde Park.

Boston’s local power bases and history of tribal politics will be tested this September as 12 candidates compete in the first wide-open mayor’s race in a generation. Most campaigns believe the electorate may be so splintered that roughly 25,000 votes — the equivalent of the population of the Cape Cod town of Yarmouth — could be enough to win one of two spots in November’s final election.

The fight for so few votes can make the election feel small, like a tug-of-war over friends and neighbors instead of a citywide debate about big ideas. Some campaigns have pushed broader issues. Bill Walczak stood on a rainy beach last week to promote his environmental blueprint. Connolly has made his plan for schools the cornerstone of his campaign. Much of the focus has been not only on fund-raising and building armies of volunteers, but campaigning door-to-door in an effort by candidates to hold their geographic base.

That’s because the race is almost like a contest to be king of a village, not mayor of a big city. Boston remains a patchwork of neighborhoods stitched together after centuries of annexations, the first addition being a part of East Boston in 1636.

DAVID L. RYAN/GLOBE STAFF

Mayoral candidates’ signs in Jamaica Plain. The preliminary election could be decided by as few as 25,000 votes.

“The village becomes the key to the kingdom,” said Jack Beatty, author of the Mayor James Michael Curley biography “The Rascal King” and a forthcoming book with Menino. “Candidates from heavy voting neighborhoods have usually prevailed.”

In this election, many of the candidates have long been kings — or queens — of their own villages, cultivating support in their neighborhoods. Voters have known some candidates as their local city councilors or state representatives. Other mayoral hopefuls have built lasting ties to residents by leading community nonprofits.

As Beatty suggests, not all villages are equal when it comes to votes. For some candidates, geography offers an advantage: Their neighbors historically cast ballots at high numbers.

For example, Consalvo’s power base in Hyde Park is part of a City Council district that includes more than 6,100 super voters — so dubbed because they have cast ballots in the last three mayoral elections. Michael P. Ross and Charles C. Yancey, two other councilors running for mayor, represent districts with roughly as many residents — but with many fewer who vote in municipal elections.

Yancey’s district in Mattapan and Dorchester has fewer than half as many super voters as Consalvo’s Hyde Park-centered district. For Ross, that number drops even lower. His district, spanning Mission Hill, Back Bay, and Fenway, includes only about 2,000 people who cast ballots in the last three mayoral elections.

Ross’s campaign advisers acknowledge they must energize people who vote in national and state races but skip city elections. They are also trying to push beyond geography to capture support from young professionals, empty nesters moving to the city, and other voters looking for someone different.

“I think today’s Boston is one in which neighborhoods don’t vote as a bloc as much,” said Ross’s campaign manager, Cayce McCabe. “I think most voters are open to hearing about candidates with new ideas and a vision for the city.”

Boston has 390,000 registered voters, but many skip municipal elections. In the last half century, there have been four open races for mayor. Turnout in those hotly contested preliminary elections averaged just 50 percent.

In this race with a dozen candidates, even home neighborhoods could be splintered. Consalvo grew up in Hyde Park, but so did two other candidates. City Councilor Felix G. Arroyo was raised there and may be a draw to the neighborhood’s influx of Latinos.

Another candidate, Suffolk District Attorney Daniel F. Conley, also grew up in Hyde Park, represented the neighborhood for a decade in the City Council, and for years, lived five blocks from Consalvo. He moved to West Roxbury in 2004, but his roots remain in Hyde Park.

“The Consalvo signs went up first,” said Robert Maida, a 56-year-old union laborer from Hyde Park leaning toward Consalvo. “But recently, I’ve seen a lot of Conley signs. It’s almost a 50-50 split.”

Hyde Park and West Roxbury are brimming with voters, but the neighborhoods in the southwest corner of Boston also feature the fiercest competition.

Connolly, Conley, and Consalvo may be fighting for support house by house, cannibalizing one another’s efforts.

Think Hyde Park and West Roxbury are crowded? In Dorchester, six candidates live within a 2-mile radius.

On Bowdoin Street, signs as big as a car for John F. Barros battle yard-by-yard with smaller placards for Charlotte Golar Richie.

The rivalry spills onto side streets such as Mount Ida Road, where two three-deckers trumpet their choice: Two small signs for Golar Richie are lashed to the front porch of a blue house; a large Barros sign dominates the porch of the tan house next door.

Similar rivalries have taken hold in Savin Hill, where Walsh lives four blocks from another mayoral candidate, Bill Walczak, cofounder of Codman Square Health Center.

“Ultimately, politics comes down to arithmetic,” said Maurice Cunningham, a political science professor at the University of Massachusetts Boston. “People are very much concentrating on their own bases. They think they can get to 25,000 [votes] and then it becomes a citywide race” in the final election.

But dominating your home base will not be enough to win a spot in November, so campaigns must work to transcend geography.

Take R + R Auto Center on Blue Hill Avenue near Franklin Park, where the chain-link fence is festooned with the signs of five mayoral candidates: radio personality Charles L. Clemons Jr., Consalvo, Barros, Walsh, and Connolly. The owner, Randy Browne, said if a candidate wants to hang a sign, that’s fine with him. Browne himself remains undecided.

“In the neighborhood, I’m hearing some talk about John Connolly and Yancey,” said Browne, 59, of Dorchester.

At an insurance office on the next corner, Edward L. Warren said there has been buzz about Clemons and Arroyo. But Warren said he is leaning toward Connolly or Yancey, the local city councilor.

For Walsh, his strong base in Dorchester has a natural connection to South Boston, a voting powerhouse that lacks a hometown candidate. Walsh’s Irish surname and organized-labor bona fides have helped attract support among Southie’s longtime residents and some union households across the city.

Walsh has also made a play for the gay community. He has repeatedly described his vote to preserve same-sex marriage as his proudest moment in the Legislature, and he won the early endorsement of state Representative Elizabeth A. Malia, who is gay and represents Jamaica Plain.

Walczak lacks the large geographic base of an elected official, but he led Codman Square Health Center for decades, putting him in contact with a large swath of Dorchester.

The campaign has tapped his network in the health care community and among nonprofits and is employing old-fashioned door knocking.

Walczak has been trying to position himself as the candidate of ideas, releasing a series of “blueprints” on education, climate change, and other issues facing the city.

Like Walczak, Barros is trying to build upon his support through his work with the Dudley Street Neighborhood Initiative in Roxbury.

His run for mayor has invigorated the Cape Verdean community. The campaign is trying to win supporters by using personal connections.

The idea is to send familiar faces — people from the same community groups, churches, barber shops — to knock on doors and engage residents.

Arroyo is the city’s first Latino candidate for mayor, and his campaign has launched television advertisements on Univision and Telemundo. He is pushing to pick up votes near his home in Jamaica Plain, with progressives, and among Latino enclaves in Hyde Park, East Boston, the South End, and elsewhere. Arroyo also has strong support among unions that represent workers in the service industry.

Beyond Hyde Park, Consalvo has also gained traction in remaining Italian sections of East Boston, where he won the endorsement of state Senator Anthony Petruccelli. East Boston has changed dramatically in recent years with a large influx of Latinos, and in Maverick Square, Consalvo signs compete for space with placards for Arroyo.

The Conley campaign expects to compete with Consalvo in Hyde Park, where the district attorney still has family roots. Advisers expect Conley to do well in his new home in West Roxbury and as district attorney, Conley has a network through the court system that transcends neighborhood boundaries.

Earlier this month, Conley held a campaign event for Latinos in Roxbury, where 50 people munched on empanadillas and mashed plantains. Conley said a few words in Spanish and introduced his brother’s wife, who comes from the Dominican Republic.

“If nothing else I said persuaded you,” Conley joked to the crowd, “I hope it’s the fact that my sister-in-law is a Latina!”

But of all the candidates, Golar Richie has perhaps the greatest opportunity to broaden her base. She is the only woman running for mayor. In Boston, 57 percent of voters in the last three mayoral elections were women.

“The one difference between her and anyone else is her village is citywide in one demographic and its makes up [almost] 60 percent of the electorate,” said Golar Richie’s campaign manager, James McGee.

In West Roxbury a few blocks from Connolly’s home, the fact that Golar Richie is a woman mattered to Sandra Cummings.

She is leaning toward Connolly because she likes his focus on education, but Cummings said she wanted to learn more about Golar Richie.

“We have a very diverse city, and I think that is a good reason to consider a woman or a minority candidate,” the 66-year-old Cummings said. “Part of me feels like I’ve seen enough white Irish guys be mayor of Boston.”

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